L1 ⚛ L1-440 ⊙ Testnet

Hull-White Interest Rate Model Calibration

Computational Finance · Interest rate modeling

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⬇ L1-440.md

# ⚛ L1 Principle — Hull-White Interest Rate Model Calibration **ID:** `L1-440` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Finance — *Interest rate modeling* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** short rate parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** market gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555259 --- ## 🧠 1. Introduction **Hull-White Interest Rate Model Calibration** is a **parameter-estimation problem** whose unknown lives in **short rate parameter vector** space, within the **Interest rate modeling** sub-domain of **Computational Finance**. Measurements consist of N/A via a **yield curve calibration** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · trinomial · tree operator; O · chi2 · swaption prices operator. Observations are corrupted by market gaussian. Existence of the recovered short_rate_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); yield_curve_inversion_error_bp dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Pointwise nonlinearity → S · trinomial · tree → O · chi2 · swaption prices → **y** (detector). ``` y = `O.chi2.swaption_prices` `S.trinomial.tree` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `S.trinomial.tree` | S · trinomial · tree operator | | `O.chi2.swaption_prices` | O · chi2 · swaption prices operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Finance | | Sub domain | Interest rate modeling | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | short_rate_parameter_vector | | Noise model | market_gaussian | | Integration axis | term_structure | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered short_rate_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); yield_curve_inversion_error_bp dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | swaption_vol_RMSE_bp | | Secondary | bond_price_RMSE_bp | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `yield_curve_calibration` **Center point:** | Parameter | Unit | Value | |---|---|---| | N tenors | — | 8 | | Vol noise bp | — | 5 | | A mean reversion | — | 0.1 | | N swaption expiries | — | 6 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N tenors | — | 3 – 30 | | Vol noise bp | — | 1 – 50 | | A mean reversion | — | 0.01 – 0.5 | | N swaption expiries | — | 3 – 20 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 8 swaption_vol_RMSE_bp | Metric | Range | |---|---| | Swaption vol rmse bp | 1 – 100 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **swaption_vol_RMSE_bp**, with κ = `2000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x362d152ac33dce79c36b54767446bcd213b07fb73f206937741e59bc965dd3e7` - **Chain tx hash:** `0x301adcd6f6de86d30066fefeef9fbaa4c0a9865b4f809a811e3422fdd57fd6ce` - **Chain block:** `41555259` --- ## File Mapping This bundle consists of: `L1-440.md`, `L1-440.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-440.md` | Source of truth — edit this | Human or LLM | | `L1-440.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-440`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-440-001 Hull-White Interest Rate Model Calibration — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555259,
  "chain_hash": "0x362d152ac33dce79c36b54767446bcd213b07fb73f206937741e59bc965dd3e7",
  "chain_tx_hash": "0x301adcd6f6de86d30066fefeef9fbaa4c0a9865b4f809a811e3422fdd57fd6ce",
  "domain": "Computational Finance",
  "hardness_fn": {
    "delta": 5,
    "kappa": 2000,
    "metric": "swaption_vol_RMSE_bp",
    "type": "epsilon_fn"
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      "license_hash": null,
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    "metric": "swaption_vol_RMSE_bp",
    "regime": "Existence of the recovered short_rate_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); yield_curve_inversion_error_bp dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market gaussian sets the irreducible data-fidelity floor.",
    "secondary": "bond_price_RMSE_bp"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Computational Finance",
    "integration_axis": "term_structure",
    "noise_model": "market_gaussian",
    "primitives": [
      "N.pointwise",
      "S.trinomial.tree",
      "O.chi2.swaption_prices"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "yield_curve_calibration",
    "solution_space": "short_rate_parameter_vector",
    "sub_domain": "Interest rate modeling",
    "title": "Hull-White Interest Rate Model Calibration"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "yield_curve_calibration"
    ],
    "allowed_omega_dimensions": [
      "N_swaption_expiries",
      "N_tenors",
      "a_mean_reversion",
      "vol_noise_bp"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "8 swaption_vol_RMSE_bp",
      "forward_operator": "yield_curve_calibration",
      "input_format": "measurement_only",
      "omega": {
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        "N_tenors": 8,
        "a_mean_reversion": 0.1,
        "vol_noise_bp": 5
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "swaption_vol_RMSE_bp": [
        1,
        100
      ]
    },
    "omega_bounds": {
      "N_swaption_expiries": [
        3,
        20
      ],
      "N_tenors": [
        3,
        30
      ],
      "a_mean_reversion": [
        0.01,
        0.5
      ],
      "vol_noise_bp": [
        1,
        50
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Interest rate modeling",
  "title": "Hull-White Interest Rate Model Calibration"
}

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